Question

Explain how the Mann-Whitney U-test is similar to a t-test for independent groups. Which other non-parametric test (that we learned in this course) is similar to the t-test for correlated groups?

Answer 1

The purpose of two sample t-test for independent groups is to test the hypothesis that the means of two groups are the same. The test assumes that the observations are normally distributed in the two groups. When this assumption is in doubt, the non-parametric Mann-Whitney U test is used as an alternative to the t-test, which doesn't rely on distributional assumptions.Mann Whitney U test can be used for testing equality of several other measures of central tendency as well, it's basically tests if the distribution of two population is same.

Assumptions for Mann-Whitney U test: Independent samples, Continuous variable, Equal variances and Identical (non-normal) distributions

Other non-parametric test that is similar to the t-test for correlated groups is Wilcoxon Signed-Rank test, It is used in those situations in which the observations are paired and you have not met the assumption of normality.

Assumptions for Wilcoxon Signed-Rank test: Differences are continuous Distribution of differences is symmetric Differences are mutually independent Differences all have the same median